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glibc  2.9
k_tanf.c
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00001 /* k_tanf.c -- float version of k_tan.c
00002  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
00003  */
00004 
00005 /*
00006  * ====================================================
00007  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00008  *
00009  * Developed at SunPro, a Sun Microsystems, Inc. business.
00010  * Permission to use, copy, modify, and distribute this
00011  * software is freely granted, provided that this notice 
00012  * is preserved.
00013  * ====================================================
00014  */
00015 
00016 #if defined(LIBM_SCCS) && !defined(lint)
00017 static char rcsid[] = "$NetBSD: k_tanf.c,v 1.4 1995/05/10 20:46:39 jtc Exp $";
00018 #endif
00019 
00020 #include "math.h"
00021 #include "math_private.h"
00022 #ifdef __STDC__
00023 static const float 
00024 #else
00025 static float 
00026 #endif
00027 one   =  1.0000000000e+00, /* 0x3f800000 */
00028 pio4  =  7.8539812565e-01, /* 0x3f490fda */
00029 pio4lo=  3.7748947079e-08, /* 0x33222168 */
00030 T[] =  {
00031   3.3333334327e-01, /* 0x3eaaaaab */
00032   1.3333334029e-01, /* 0x3e088889 */
00033   5.3968254477e-02, /* 0x3d5d0dd1 */
00034   2.1869488060e-02, /* 0x3cb327a4 */
00035   8.8632395491e-03, /* 0x3c11371f */
00036   3.5920790397e-03, /* 0x3b6b6916 */
00037   1.4562094584e-03, /* 0x3abede48 */
00038   5.8804126456e-04, /* 0x3a1a26c8 */
00039   2.4646313977e-04, /* 0x398137b9 */
00040   7.8179444245e-05, /* 0x38a3f445 */
00041   7.1407252108e-05, /* 0x3895c07a */
00042  -1.8558637748e-05, /* 0xb79bae5f */
00043   2.5907305826e-05, /* 0x37d95384 */
00044 };
00045 
00046 #ifdef __STDC__
00047        float __kernel_tanf(float x, float y, int iy)
00048 #else
00049        float __kernel_tanf(x, y, iy)
00050        float x,y; int iy;
00051 #endif
00052 {
00053        float z,r,v,w,s;
00054        int32_t ix,hx;
00055        GET_FLOAT_WORD(hx,x);
00056        ix = hx&0x7fffffff;  /* high word of |x| */
00057        if(ix<0x31800000)                  /* x < 2**-28 */
00058            {if((int)x==0) {               /* generate inexact */
00059               if((ix|(iy+1))==0) return one/fabsf(x);
00060               else return (iy==1)? x: -one/x;
00061            }
00062            }
00063        if(ix>=0x3f2ca140) {                      /* |x|>=0.6744 */
00064            if(hx<0) {x = -x; y = -y;}
00065            z = pio4-x;
00066            w = pio4lo-y;
00067            x = z+w; y = 0.0;
00068        }
00069        z      =  x*x;
00070        w      =  z*z;
00071     /* Break x^5*(T[1]+x^2*T[2]+...) into
00072      *   x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
00073      *   x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
00074      */
00075        r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
00076        v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
00077        s = z*x;
00078        r = y + z*(s*(r+v)+y);
00079        r += T[0]*s;
00080        w = x+r;
00081        if(ix>=0x3f2ca140) {
00082            v = (float)iy;
00083            return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
00084        }
00085        if(iy==1) return w;
00086        else {        /* if allow error up to 2 ulp, 
00087                         simply return -1.0/(x+r) here */
00088      /*  compute -1.0/(x+r) accurately */
00089            float a,t;
00090            int32_t i;
00091            z  = w;
00092            GET_FLOAT_WORD(i,z);
00093            SET_FLOAT_WORD(z,i&0xfffff000);
00094            v  = r-(z - x);  /* z+v = r+x */
00095            t = a  = -(float)1.0/w; /* a = -1.0/w */
00096            GET_FLOAT_WORD(i,t);
00097            SET_FLOAT_WORD(t,i&0xfffff000);
00098            s  = (float)1.0+t*z;
00099            return t+a*(s+t*v);
00100        }
00101 }